Question: Solve for $x$ and $y$ using elimination. ${x+5y = 16}$ ${-x+2y = -2}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $7y = 14$ $\dfrac{7y}{{7}} = \dfrac{14}{{7}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x+5y = 16}\thinspace$ to find $x$ ${x + 5}{(2)}{= 16}$ $x+10 = 16$ $x+10{-10} = 16{-10}$ ${x = 6}$ You can also plug ${y = 2}$ into $\thinspace {-x+2y = -2}\thinspace$ and get the same answer for $x$ : ${-x + 2}{(2)}{= -2}$ ${x = 6}$